A Differentiable Ecosystem Modeling Framework for Highly Efficient Forward and Inverse Problems

Photosynthesis is an essential process that plays an important role in the whole ecosystem due to being a crucial member in the carbon, nitrogen, and water cycles. The response of these cycles to a changing climate can be estimated by ecosystem models which are an important component of earth system models. Ecosystem processes are described by many coupled nonlinear equations, the solution to which can be both computationally expensive and algorithmically complex. Yet, at the same time, they are characterized by myriad parameters that are difficult to determine. Here we propose an ecosystem modeling framework suitable for large-scale inverse problems, e.g., for large-scale parameterization. The package automatically solves the nonlinear equations in ecosystem modeling, e.g., for photosynthesis. For this purpose, we leverage one of the available process-based ecosystem models which is the Functionally Assembled Terrestrial Ecosystem Simulator known as FATES and supported in both the Community Land Model of the Community Terrestrial Systems Model (CLM-CTSM) and in the Energy Exascale Earth Systems Model (E3SM) Land Model (ELM). Meanwhile, we can intermingle process descriptions with neural networks to enable the learning of parameterization or processes. The system is implemented on two platforms including Julia and PyTorch. We first demonstrate the power of the package with the Fates module and show it was able to recover some hypothetical parameter values for different plant functional types (PFTs). Then, we show that, by learning from a real-world dataset, for many of the PFTs, the package found parameters that are correlated with the database but performed better than the literature values.